On the zero forcing number and propagation time of oriented graphs

Zero forcing is a process of coloring in a graph in time steps known as propagation time. These graph-theoretic parameters have diverse applications in computer science, electrical engineering and mathematics itself. The problem of evaluating these parameters for a network is known to be NP-hard. Th...

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Bibliographic Details
Published inAIMS mathematics Vol. 6; no. 2; pp. 1833 - 1850
Main Authors Hayat, Sakander, Muhammad Afzal Siddiqui, Hafiz, Imran, Muhammad, Muhammad Ikhlaq, Hafiz, Cao, Jinde
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2021
Subjects
graph applications
graph coloring
oriented graphs
propagation time
zero forcing process
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Summary:Zero forcing is a process of coloring in a graph in time steps known as propagation time. These graph-theoretic parameters have diverse applications in computer science, electrical engineering and mathematics itself. The problem of evaluating these parameters for a network is known to be NP-hard. Therefore, it is interesting to study these parameters for special families of networks. Perila et al. (2017) studied properties of these parameters for some basic oriented graph families such as cycles, stars and caterpillar networks. In this paper, we extend their study to more non-trivial structures such as oriented wheel graphs, fan graphs, friendship graphs, helm graphs and generalized comb graphs. We also investigate the change in propagation time when the orientation of one edge is flipped.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.2021111